American officials and diplomats said the new strategy is still being discussed, but initial efforts may focus on passing United Nations sanctions against those responsible for the chemical weapons attack three years ago.
A UN-backed panel is expected in the next few weeks to present new findings about the deadly chemical attacks in the Damascus suburb of Ghouta in 2013.
Syrian opposition groups and their western allies claim the nerve gas attacks were launched by the Syrian government. Damascus rejects the allegation, saying the attack was carried out by militants operating inside the country to draw in foreign intervention. Subsequent investigations by the UN and Russia backed Syria’s assertions.
Most of Syrian President Bashar al-Assad's top government and military officials are already the subjects of US travel bans and assets freezes.
However, Washington’s efforts to add sanctions against Damascus could force Moscow to wield its veto in the UN Security Council.
"What we are doing now is a different type of diplomacy -- one which might be more robust -- it could be resolutions which are designed to put pressure on them," a US diplomat at the UN said.
"The strategy that we are on is to try to change Russian behavior and let's face it, we have not been very successful at that in the year that they have been militarily supporting Assad," the diplomat added.
Russia has been supporting the Syrian government in its campaign against terrorist groups operating in the country.
Syrian government forces, backed by the Russian air campaign, have managed to gain more ground against foreign-sponsored militants.
On Monday, the United States suspended bilateral channels with Moscow that were established to maintain the cessation of hostilities in the war-torn country amid rising tensions over the embattled city of Aleppo. The US has been working with Russia for months to try to secure a ceasefire in Syria.